Question

Write a recursive rule for the sequence: 1, 2, 3, 4, 9, -27, 81, -243.

A. a_n = 9, a_n = -3, a_n-1
B. a_n = 9, a_n = 0, a_n-1 - 2
C. a_n = 9, a_n = -2, a_n-1
D. a_n = 9, a_n = 4, a_n-1 - 3

Answer 1

A recursive rule for the given sequence is established by setting the first four terms as base cases and defining subsequent terms as the product of -3 and the term before it.

Step-by-step explanation:

The question asks us to write a recursive rule for the sequence: 1, 2, 3, 4, 9, -27, 81, -243. Looking at the sequence, there is a pattern where starting from the fifth term, each term is the previous term multiplied by -3. To express this pattern in a recursive form, we set the first four terms as the base cases, a_1 = 1, a_2 = 2, a_3 = 3, and a_4 = 4. Then, for n > 4, the rule is a_n = -3 × a_{n-1}. This rule shows that each term (from the fifth term onwards) is the product of -3 and the immediately preceding term in the sequence.